Simplify the following expression: $ q = \dfrac{5}{9} + \dfrac{9k}{-6k - 6} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-6k - 6}{-6k - 6}$ $ \dfrac{5}{9} \times \dfrac{-6k - 6}{-6k - 6} = \dfrac{-30k - 30}{-54k - 54} $ Multiply the second expression by $\dfrac{9}{9}$ $ \dfrac{9k}{-6k - 6} \times \dfrac{9}{9} = \dfrac{81k}{-54k - 54} $ Therefore $ q = \dfrac{-30k - 30}{-54k - 54} + \dfrac{81k}{-54k - 54} $ Now the expressions have the same denominator we can simply add the numerators: $q = \dfrac{-30k - 30 + 81k}{-54k - 54} $ $q = \dfrac{51k - 30}{-54k - 54}$ Simplify the expression by dividing the numerator and denominator by -3: $q = \dfrac{-17k + 10}{18k + 18}$